Complexes of Directed Trees
Complexes of Directed Trees
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有向树的复合体
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
D. Kozlov
中科院分区：
文献类型：
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作者：
D. Kozlov
对每个有向图G，可以关联一个由有向子林组成的复数？(G)。这一结构是由R.Stanley提出的，在完全双向图Gn的情况下尤其重要，它导致研究对称群的一些有趣的表示，并(通过Stanley？Reisner对应)对应于一个有趣的商环。我们的主要结果表明？(GN)是可壳的，特别是Cohen？Macaulay，这可以进一步解释为？(GN)的Stanley？Reisner环是Cohen？Macaulay。此外，当G本质上是树和G是双向圈时，通过计算？(G)的同调群，我们触及了图的组合性质和相关复形的拓扑性质相互作用的一般问题。
To every directed graph G one can associate a complex ?(G) consisting of directed subforests. This construction, suggested to us by R. Stanley, is especially important in the case of a complete double directed graph Gn, where it leads to the study of some interesting representations of the symmetric group and corresponds (via the Stanley?Reisner correspondence) to an interesting quotient ring. Our main result states that ?(Gn) is shellable, in particular, Cohen?Macaulay, which can be further translated to say that the Stanley?Reisner ring of ?(Gn) is Cohen?Macaulay. Besides that, by computing the homology groups of ?(G) for the cases when G is essentially a tree and when G is a double directed cycle, we touch upon the general question of the interaction of the combinatorial properties of a graph and the topological properties of the associated complex.